Chapter 12: Structures & Properties of Ceramics ISSUES TO ADDRESS... • How do the crystal structures of ceramic materials differ from those for metals? • How do point defects in ceramics differ from those defects found in metals? • How are impurities accommodated in the ceramic lattice? • In what ways are ceramic phase diagrams different from phase diagrams for metals? • How are the mechanical properties of ceramics measured, and how do they differ from those for metals?

Atomic Bonding in Ceramics -- Can be ionic and/or covalent in character. -- % ionic character increases with difference in electronegativity of atoms. • Degree of ionic character may be large or small: CaF2: large SiC: small Adapted from Fig. 2.7, Callister & Rethwisch 8e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.)

Ceramic Crystal Structures Oxide structures oxygen anions larger than metal cations close packed oxygen in a lattice (usually FCC) cations fit into interstitial sites among oxygen ions

Factors that Determine Crystal Structure 1. Relative sizes of ions – Formation of stable structures: --maximize the # of oppositely charged ion neighbors. - + unstable - + - + Adapted from Fig. 12.1, Callister & Rethwisch 8e. stable stable 2. Maintenance of Charge Neutrality : --Net charge in ceramic should be zero. --Reflected in chemical formula: CaF 2 : Ca 2+ cation F - anions + A m X p m, p values to achieve charge neutrality

Coordination # and Ionic Radii cation anion • Coordination # increases with To form a stable structure, how many anions can surround around a cation? Adapted from Fig. 12.2, Callister & Rethwisch 8e. Adapted from Fig. 12.3, Callister & Rethwisch 8e. Adapted from Fig. 12.4, Callister & Rethwisch 8e. ZnS (zinc blende) NaCl (sodium chloride) CsCl (cesium r cation anion Coord # < 0.155 2 linear 0.155 - 0.225 3 triangular 0.225 - 0.414 4 tetrahedral 0.414 - 0.732 6 octahedral 0.732 - 1.0 8 cubic Adapted from Table 12.2, Callister & Rethwisch 8e.

Computation of Minimum Cation-Anion Radius Ratio Determine minimum rcation/ranion for an octahedral site (C.N. = 6) a = 2ranion

Bond Hybridization Bond Hybridization is possible when there is significant covalent bonding hybrid electron orbitals form For example for SiC XSi = 1.8 and XC = 2.5 ~ 89% covalent bonding Both Si and C prefer sp3 hybridization Therefore, for SiC, Si atoms occupy tetrahedral sites

Example Problem: Predicting the Crystal Structure of FeO • On the basis of ionic radii, what crystal structure would you predict for FeO? Cation Anion Al 3+ Fe 2 + Ca 2+ O 2- Cl - F Ionic radius (nm) 0.053 0.077 0.069 0.100 0.140 0.181 0.133 • Answer: based on this ratio, -- coord # = 6 because 0.414 < 0.550 < 0.732 -- crystal structure is NaCl Data from Table 12.3, Callister & Rethwisch 8e.

Rock Salt Structure Same concepts can be applied to ionic solids in general. Example: NaCl (rock salt) structure rNa = 0.102 nm rCl = 0.181 nm rNa/rCl = 0.564 cations (Na+) prefer octahedral sites Adapted from Fig. 12.2, Callister & Rethwisch 8e.

MgO and FeO MgO and FeO also have the NaCl structure O2- rO = 0.140 nm Mg2+ rMg = 0.072 nm rMg/rO = 0.514 cations prefer octahedral sites Adapted from Fig. 12.2, Callister & Rethwisch 8e. So each Mg2+ (or Fe2+) has 6 neighbor oxygen atoms

AX Crystal Structures AX–Type Crystal Structures include NaCl, CsCl, and zinc blende Cesium Chloride structure:  Since 0.732 < 0.939 < 1.0, cubic sites preferred So each Cs+ has 8 neighbor Cl- Adapted from Fig. 12.3, Callister & Rethwisch 8e.

AX2 Crystal Structures Fluorite structure Calcium Fluorite (CaF2) Cations in cubic sites UO2, ThO2, ZrO2, CeO2 Antifluorite structure – positions of cations and anions reversed Adapted from Fig. 12.5, Callister & Rethwisch 8e.

ABX3 Crystal Structures Perovskite structure Ex: complex oxide BaTiO3 Adapted from Fig. 12.6, Callister & Rethwisch 8e.

VMSE: Ceramic Crystal Structures

Density Computations for Ceramics Number of formula units/unit cell Avogadro’s number Volume of unit cell = sum of atomic weights of all cations in formula unit = sum of atomic weights of all anions in formula unit

Silicate Ceramics Most common elements on earth are Si & O SiO2 (silica) polymorphic forms are quartz, crystobalite, & tridymite The strong Si-O bonds lead to a high melting temperature (1710ºC) for this material Si4+ O2- Adapted from Figs. 12.9-10, Callister & Rethwisch 8e crystobalite

Silicates Bonding of adjacent SiO44- accomplished by the sharing of common corners, edges, or faces Adapted from Fig. 12.12, Callister & Rethwisch 8e. Mg2SiO4 Ca2MgSi2O7 Presence of cations such as Ca2+, Mg2+, & Al3+ 1. maintain charge neutrality, and 2. ionically bond SiO44- to one another

Glass Structure • Basic Unit: Glass is noncrystalline (amorphous) • Fused silica is SiO2 to which no impurities have been added • Other common glasses contain impurity ions such as Na+, Ca2+, Al3+, and B3+ Si0 4 tetrahedron 4- Si 4+ O 2 - • Quartz is crystalline SiO2: Si 4+ Na + O 2 - (soda glass) Adapted from Fig. 12.11, Callister & Rethwisch 8e.

Layered Silicates Layered silicates (e.g., clays, mica, talc) SiO4 tetrahedra connected together to form 2-D plane A net negative charge is associated with each (Si2O5)2- unit Negative charge balanced by adjacent plane rich in positively charged cations Adapted from Fig. 12.13, Callister & Rethwisch 8e.

Layered Silicates (cont.) Kaolinite clay alternates (Si2O5)2- layer with Al2(OH)42+ layer Adapted from Fig. 12.14, Callister & Rethwisch 8e. Note: Adjacent sheets of this type are loosely bound to one another by van der Waal’s forces.

Polymorphic Forms of Carbon Diamond tetrahedral bonding of carbon hardest material known very high thermal conductivity large single crystals – gem stones small crystals – used to grind/cut other materials diamond thin films hard surface coatings – used for cutting tools, medical devices, etc. Adapted from Fig. 12.15, Callister & Rethwisch 8e.

Polymorphic Forms of Carbon (cont) Graphite layered structure – parallel hexagonal arrays of carbon atoms weak van der Waal’s forces between layers planes slide easily over one another -- good lubricant Adapted from Fig. 12.17, Callister & Rethwisch 8e.

Polymorphic Forms of Carbon (cont) Fullerenes and Nanotubes Fullerenes – spherical cluster of 60 carbon atoms, C60 Like a soccer ball Carbon nanotubes – sheet of graphite rolled into a tube Ends capped with fullerene hemispheres Adapted from Figs. 12.18 & 12.19, Callister & Rethwisch 8e.

Point Defects in Ceramics (i) • Vacancies -- vacancies exist in ceramics for both cations and anions • Interstitials -- interstitials exist for cations -- interstitials are not normally observed for anions because anions are large relative to the interstitial sites Cation Interstitial Vacancy Anion Adapted from Fig. 12.20, Callister & Rethwisch 8e. (Fig. 12.20 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.)

Point Defects in Ceramics (ii) • Frenkel Defect -- a cation vacancy-cation interstitial pair. • Shottky Defect -- a paired set of cation and anion vacancies. Shottky Defect: Frenkel Defect Adapted from Fig.12.21, Callister & Rethwisch 8e. (Fig. 12.21 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.) • Equilibrium concentration of defects

Imperfections in Ceramics • Electroneutrality (charge balance) must be maintained when impurities are present Na + Cl - • Ex: NaCl • Substitutional cation impurity without impurity Ca 2+ impurity with impurity Na + cation vacancy • Substitutional anion impurity without impurity O 2- impurity Cl - an ion vacancy with impurity

Ceramic Phase Diagrams MgO-Al2O3 diagram:  Adapted from Fig. 12.25, Callister & Rethwisch 8e.

Mechanical Properties Ceramic materials are more brittle than metals. Why is this so? Consider mechanism of deformation In crystalline, by dislocation motion In highly ionic solids, dislocation motion is difficult few slip systems resistance to motion of ions of like charge (e.g., anions) past one another

Flexural Tests – Measurement of Elastic Modulus • Room T behavior is usually elastic, with brittle failure. • 3-Point Bend Testing often used. -- tensile tests are difficult for brittle materials. F L/2 d = midpoint deflection cross section R b d rect. circ. Adapted from Fig. 12.32, Callister & Rethwisch 8e. • Determine elastic modulus according to: F x linear-elastic behavior d slope = (rect. cross section) (circ. cross section)

Flexural Tests – Measurement of Flexural Strength • 3-point bend test to measure room-T flexural strength. F L/2 d = midpoint deflection cross section R b d rect. circ. location of max tension Adapted from Fig. 12.32, Callister & Rethwisch 8e. • Flexural strength: • Typical values: Data from Table 12.5, Callister & Rethwisch 8e. Si nitride Si carbide Al oxide glass (soda-lime) 250-1000 100-820 275-700 69 304 345 393 Material s fs (MPa) E(GPa) (rect. cross section) (circ. cross section)

SUMMARY • Interatomic bonding in ceramics is ionic and/or covalent. • Ceramic crystal structures are based on: -- maintaining charge neutrality -- cation-anion radii ratios. • Imperfections -- Atomic point: vacancy, interstitial (cation), Frenkel, Schottky -- Impurities: substitutional, interstitial -- Maintenance of charge neutrality • Room-temperature mechanical behavior – flexural tests -- linear-elastic; measurement of elastic modulus -- brittle fracture; measurement of flexural modulus